Topology Signal Processing as promising direction to Combine Topology, Physics, Information Theory and Machine Learning

This section of the project will include materials and source codes related to Topological (Homology/Cohomology) Signal Processing, as well as its data-driven approaches (including machine learning techniques such as super-resolution deep neural networks, graphical probabilistic models, and tensor contractions) and model-driven approaches (such as topology complex and thickening to smooth manifold optimization).

Quantum and Classical ML for DNN using Ising models (Markov Random Fields, Spin-glass) detailed described at repository https://github.com/Lcrypto/Classical-and-Quantum-Topology-ML-toric-spherical

Below is a simple example implemented in MATLAB that uses a Convolutional Neural Network with 6 layers (conv2d -> relu) for channel estimation. The code can be found at https://github.com/Lcrypto/Topology-Signal-Processing/tree/master/SISO%20Example%20Matlab%206%20Layers%20CNN%2051%20Rbs Matlab 6 Layers CNN 51 Rbs, and it uses a Single Input Single Output (SISO) Non-Line-of-Sight (NLOS) 5G NR Downlink TDL-C Channel with 51 Resource Blocks (RBs), Delay Spread = 3e-7, Maximum Doppler Shift = 30 Hz, and SNRdB = 7.

Please note that the presentation titled "MMMA-2019_19_8_19_final.pdf" in the "Topology-Signal-Processing" repository on GitHub represents ideas related to Super Resolution Deep Neural Network Wireless Channel Estimation and Sparse Dictionary Optimization for Faster-than-Nyquist Sampling, as well as its connection to topology and machine learning. The presentation was delivered at The 5th International Conference on Matrix Methods In Mathematics and applications (MMMA 2019) in August 2019, and you can find more information about the conference at https://www.skoltech.ru/en/2019/08/the-5th-international-conference-on-matrix-methods-in-mathematics-and-applications/.

Furthermore, publication titled "Wireless Channels Topology Invariant as Mathematical Foundation of Neural Network Channel Estimation Transfer Learning Properties" adds valuable content to this project. It was presented at the 43rd International Conference on Telecommunications and Signal Processing (TSP) in 2020 and published by IEEE Xplore. You can find the paper at https://ieeexplore.ieee.org/document/9163528.

In paper V. S. Usatyuk and S. I. Egorov, "2D/3D ResNet Deep Neural Network for 4G and 5G NR Wireless Channel Estimation," 2023 25th International Conference on Digital Signal Processing and its Applications (DSPA), Moscow, Russian Federation, 2023, pp. 1-4 we consider application for more wideband compare to 1 RB for 4G, 20 RBs application for channel estimation of NEW RADIO channel (5G 3gpp release 15). https://ieeexplore.ieee.org/document/10113403